Question

if x sin³ Q + y cos³ Q = sin Q × cos Q and x sin Q = y cos Q, prove that x² + y² = 1

(Board term -1 , 2011 )

Answer 1

hey... here's ur solution !!
GIVEN,
x sin Q = y cos Q
x = y cos Q / sin Q....................... (1)
and,

x sin³Q + y cos³ Q = sinQ cos Q.............. (2)

Elimating x from equ (1) nd (2)


(y cos Q / sinQ) × sin³ Q + y cos ³ Q = sinQ cosQ

y cos Q sin² Q + y cos³ Q = sinQ cosQ

➡ y cos Q sin²Q + y cos³ Q = sin Q cos Q

➡y cosQ ( sin²Q + cos²Q ) = sinQ cosQ

➡y = sinQ...........................(3)

Substituting this value of y in eq. (3)

x = cosQ............................... (4)


squaring and adding eq. (3) and (4), we get

x² + y² = cos²Q + sin²Q = 1


❇Hence Prove ❇

Answer 2

Answer:

For answer refer Image!

Step-by-step explanation:

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